Various systems exist for the purpose of positioning one or more substrates in one or more locations to allow operations to be performed on the substrate or substrates. Some systems, such as alignment systems, attempt to position substrates by directly aligning one or more patterns on the substrates with the goal of a zero-length displacement. Moiré patterns or other particular patterns such as a box and a cross may be used for this purpose. However, the use of such patterns, particularly with respect to the precision gratings required to produce moiré or diffraction patterns, may add costs to the manufacturing process.
With existing alignment systems, the positioning of substrates may be poorly quantized and may not be useful in instances where a non-zero displacement is desired. Further, due to process variations, alignment systems that compare patterns across different substrates may run into performance limitations. It would be desirable to be able to accurately quantize the position or positions of substrates.